Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (f (x))
> Consider the rectangle in Exercise 1. Write an expression for the area. Write an equation expressing the fact that the perimeter is 30 centimeters. Rectangle with height = 3- width
> Consider the rectangle in Exercise 1. Write an expression for the perimeter. If the area is 25 square feet, write this fact as an equation. Rectangle with height = 3- width
> Assign variables to the dimensions of the geometric object. Cylinder with height = diameter
> Assign variables to the dimensions of the geometric object. Сyinder
> Compute the numbers. 025
> Compute the numbers. 1100
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. g(x)h(x)
> Compute the numbers. (-2)3
> Compute the numbers. 33
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.23E-6
> Decide which curves are graphs of functions.
> Convert the numbers from graphing calculator form to standard form (that is, without E). 1.35E13
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.103E-4
> Convert the numbers from graphing calculator form to standard form (that is, without E). 5E-5
> Velocity When a car’s brakes are slammed on at a speed of x miles per hour, the stopping distance is 1 20x2 feet. Show that when the speed is doubled the stopping distance increases fourfold.
> Semiannual Compound Assume that a $1000 investment earns interest compounded semiannually. Express the value of the investment after 2 years as a polynomial in the annual rate of interest r.
> Assume that a $500 investment earns interest compounded quarterly. Express the value of the investment after 1 year as a polynomial in the annual rate of interest r.
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ 12
> Assume that a couple invests $4000 each year for 4 years in an investment that earns 8% compounded annually. What will the value of the investment be 8 years after the first amount is invested?
> Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the daughter’s 18th birthday?
> Calculate the compound amount from the given data. principal = $1500, compounded daily, 3 years, annual rate = 6%
> Calculate the compound amount from the given data. principal = $1500, compounded daily,1 year, annual rate = 6%
> Decide which curves are graphs of functions.
> Calculate the compound amount from the given data. principal = $500, compounded monthly,1 year, annual rate = 4.5%
> Calculate the compound amount from the given data. principal = $100, compounded monthly, 10 years, annual rate = 5%
> Calculate the compound amount from the given data. principal = $20,000, compounded quarterly, 3 years, annual rate = 12%
> Calculate the compound amount from the given data. principal = $50,000, compounded quarterly, 10 years, annual rate = 9.5%
> Calculate the compound amount from the given data. principal = $700, compounded annually, 8 years, annual rate = 8%
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x)g(x)
> Calculate the compound amount from the given data. principal = $500, compounded annually, 6 years, annual rate = 6%
> Evaluate f (4). f (x) = x0
> Evaluate f (4). f (x) = x-5/2
> Evaluate f (4). f (x) = x-1/2
> Evaluate f (4). f (x) = x3/2
> Decide which curves are graphs of functions. -x
> Draw the following intervals on the number line. [ -2, √2)
> Evaluate f (4). f (x) = x1/2
> Evaluate f (4). f (x) = x-1
> Evaluate f (4). f (x) = x3
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (t) - h(t)
> Evaluate f (4). f (x) = x2
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a/√b = √ (a/b).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a * √b = √(ab).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √ (x/y) - √ (y/x) = √xy ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. x-1/4 + 6x1/4 = x-1/4( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Decide which curves are graphs of functions.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(g(x))
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x) - g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g (f (x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. 3√ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)/ g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)g(x)]3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(x) / f (x)
> Sketch the graph of the function. f (x) = 1 / f(x) = x + 1
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x) / g(x)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 6 / x – 6, g(x) = x – 6 / x + 6
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ -1 and x < 8
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x)g(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-32y-5)3/5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-27x5)2/3 / x3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 / x2y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √x (1/4x)5/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-8y9)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (16x8)-3/4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 / yx-5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> Sketch the graph of the function. f (x) = √(x + 1)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 5 / x – 10, g(x) = x / x + 10
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x2 / x5y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (3x2 / 2y)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-3x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-4 / x3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x3 / y-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -x3y / -xy
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -3x / 15x4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (2x)4
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) =-x / x + 3, g(x) = x / x + 5
> Sketch the graph of the function. f (x) = 2x2 - 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-3 * x7
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x5 * (y2 / x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √(1 + x) * (1 + x)3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3y5)4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x/y)-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 / y2)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3 * y6)1/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-1/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1/x-3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x / x - 8, g(x) =-x / x - 4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 * y5)/ xy2
> Sketch the graph of the function. f (x) = x2 + 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x1/3)6
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (xy)6
> Use the laws of exponents to compute the numbers. (61/2)0
